2 papers
math.NA2026
Fortin operators for DPG advection discretizations
Pablo Cortés Castillo, Jay Gopalakrishnan
We construct Fortin operators for discontinuous Petrov-Galerkin (DPG) discretizations of the advection equation with a piecewise constant divergence-free advection vector , on s…
math.NA2025
DPG loss functions for learning parameter-to-solution maps by neural networks
Pablo Cortés Castillo, Wolfgang Dahmen, Jay Gopalakrishnan
We develop, analyze, and experimentally explore residual-based loss functions for machine learning of parameter-to-solution maps in the context of parameter-dependent families of p…